Theme Essential Question: How can you apply and extend the usage of rational numbers when dealing with real world problems?
Essential Questions:
How do you apply your strategies/algorithms used in adding integers to adding rational numbers?
How do you apply your strategies/algorithms used in subtracting integers to subtracting rational numbers?
How can you describe situations in which opposite quantities combine to make 0?
How do you use the concept of absolute value to determine distance between two rational numbers?
Standards: 7. NS.1: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
7.NS.1a: Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has a 0 charge because its two constituents are oppositely charged.
7. NS.1b: Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts
7.NS.1c: Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
7.NS.1d: Apply properties of operations as strategies to add and subtract rational numbers.
Objectives:
The student will add rational numbers with the same sign and with different signs.
The student will subtract rational numbers with the same sign and with different signs.
The student will describe situations in which opposite quantities combine to make zero, (additive inverse).
The student will use the concept of absolute value to determine distance between two rational numbers.
Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team
During the first week, the students’ activities lead them to develop strategies/algorithms for integer operations. This week’s lesson expands this knowledge to include all rational numbers. This lesson is based on the work done in 6th grade with addition/subtraction of positive fractions in conjunction to the work done with addition/subtraction of integers.
Continue working with students on Mathematical Practice #7, looking for and making use of structure. The success of this lesson depends on the students’ ability to connect the structure that helped them develop their strategies/algorithms in week 1 and their prior know of fractional addition/subtractions. It is an opportunity time to introduce Mathematical Practice #2, reason abstractly and quantitatively. Both reference books, Oncore Mathematics and Mastering the Common core, will provide real world problems in order to support the deep and application of addition/subtraction of rational numbers.
Background Information Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials at http://www.azed.gov/educator-certification/
Assessment: Product
This will be an ongoing product that will be developed during each week of the unit. Continue foldables this week with long division.
Foldable Make a foldable with five divided sections (3 pieces of paper needed). Students will create a section for each of the following:
Addition- Have written rule and examples using integers, fractions, and decimals.
Subtraction- Have written rule and examples using integers, fractions, and decimals.
Multiplication- Have written rule and examples using integers, fractions, and decimals.
Division- Have written rule and examples using integers, fractions, and decimals.
Long Division- Have written rule and examples.
Key Questions
What is the result of adding two positive rational numbers? Two negative rational numbers? One negative and one positive rational numbers?
What is the result of subtracting two positive rational numbers? Two negative rational numbers? One negative and one positive rational numbers?
What kind of change do you get when you add a pair of additive inverses?
What is the additive inverse of a negative number?
What is the additive inverse of a positive number?
What is the additive inverse of zero?
How do you find the distance between two rational numbers?
Observable Student Behaviors
The student can demonstrate the application of their algorithms given an addition or subtraction problem.
The student can identify the additive inverse of a rational number and provide a viable explanation as to why it is identified as such.
The student can find the distance between two rational numbers.
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Vocabulary:
Math
Rational Number Additive Inverse Decimals Fractions Integers Negative Numbers Number Line Opposites Positive Numbers
Suggested Activities:
On Core Mathematics 1.2 p. 7-10, 1.3 p. 11-14
Mastering the COMMON CORE in Mathematics Grade 7by American Book Company,
3.3.8, p. 24-30, Chapter Review/Test p. 31-33
Teaching the Common Core Math Standards with Hands-On ActivitiesGizmo Correlation
NS.1 p. 90
Gizmo Element Builder
Use protons, neutrons, and electrons to build elements. As the number of protons, neutrons, and electrons changes, information such as the name and symbol of the element, the Z, N, and A numbers, the electron dot diagram, and the group and period from the periodic table are shown. Each element is classified as a metal, metalloid, or nonmetal, and its state at room temperature is also given. Use a number line to compare numbers. Change values by dragging points on the number line. Compare the opposites and absolute values of the numbers.
Adding and Subtracting Integers with Chips
Use chips to model addition and subtraction of positives and negatives. Explore the effect of zero pairs. See how to use zero pairs to help special cases of addition and subtraction.
Adding and Subtracting Integers
Add and subtract integers on a number line using dynamic arrows.
The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
JBHM
Glencoe Mathematics Application and Concepts Course 2, 3.4-3.5 (Integers) p.118-133
Glencoe Pre-Algebra, 5.5-5.7 (fractions) p. 220-236
Perry the Penguin needs 9 clams to buy an ice scooter -- but he's not very good at saving. As Perry earns, spends, finds, loses, and borrows clams, a simple line graph demonstrates the concept of negative numbers.
Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annotated Lists of Children's Literature including the math concepts and grade levels.
"If this is an adventure, we should just plunge in..."
When thirteen-year-old cousins Ivan and Daphne go on a treasure hunt in the rain one summer day, they never expect to stumble into a whole new world where words and numbers run wild. After the cousins outwit a plague of punctuation, grateful villagers beg them to find Lexicon's missing children, who have been enticed away by dancing lights in the sky. Trekking between villages in search of clues, the cousins encounter a talking thesaurus, a fog of forgetting, the Mistress of Metaphor, a panel of poets, feuding parts of speech, and the illogical mathematicians of Irrationality. When a careless Mathemystical reflects them across the border into the ominous Land of Night, their peril deepens. Kidnapped, imprisoned, and mesmerized—with time running out—will Ivan and Daphne find a way to solve the mystery of the lights in the sky and restore the lost children of Lexicon to their homes? Lost in Lexicon will whisk children away into an interactive and magical world of learning.
Math is a critical part of our everyday lives; we use it dozens of times daily and wish we understood it better. The second title in the 101 Things Everyone Should Know series, this book makes understanding math easy and fun! Using an appealing question and answer format, this book is perfect for kids, grown-ups and anyone interested in the difference between an Olympic event score of 9.0 and Richter scale score of 9.0.
Middle & High School: Literature in Mathematics Many books include websites with lesson ideas. http://sci.tamucc.edu/~eyoung/middle_school_literature.html Lesson Plans for Using Literature in Middle and High School Mathematics (developed by Leonor and edited by Elaine)
The teaching Channel currently offers videos of K-12 mathematics teaching aligned with the Common Core Sate Standards, which would be perfect for professional development with teacher teams.
http://illuminations.nctm.org/LessonDetail.aspx?ID=L566 Students typically learn about the concepts of identity, inverse, commutativity, and associativity by exploring the four basic operations (+, –, ×, and ÷) with integers. In this lesson, students investigate these concepts using a geometric model. Moves are performed with a rectangle, and the results of an operation that combines two moves are analyzed. Students determine if the operation is commutative or associative; if an identity element exists; or if there are inverses for any of the moves.
http://illuminations.nctm.org/LessonDetail.aspx?ID=L734 In this lesson, students will adapt expressions that add or subtract two signed integers. This lesson builds on the previous lesson in the unit, where students add/subtract just a positive integer from a signed integer.
Fun with Baseball Stats
http://illuminations.nctm.org/LessonDetail.aspx?ID=L257 The following grades 6-8 activities allow students to explore statistics surrounding baseball. They are exposed to connections between various mathematical concepts and see where this mathematics is used in areas with which they are familiar. This lesson plan is adapted from the May 1996 edition of Mathematics Teaching in the Middle School.
Power Up
http://illuminations.nctm.org/LessonDetail.aspx?ID=L699 Using old batteries and a voltage sensor, students get a real feel of the meaning of negative and positive numbers. Students explore addition of signed numbers by placing batteries end to end (in the same direction or opposite directions) and observe the sum of the batteries’ voltages.
http://illuminations.nctm.org/LessonDetail.aspx?ID=L252 In this lesson, students develop number sense through a series of three hands-on activities. Students explore the following concepts: the magnitude of a million, fractions between 0 and 1, and the effect of decimal operations.
Content: Adding and Subtracting Rational Numbers
Theme Essential Question:
How can you apply and extend the usage of rational numbers when dealing with real world problems?
Essential Questions:
Standards:
7. NS.1: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
Objectives:
Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team
During the first week, the students’ activities lead them to develop strategies/algorithms for integer operations. This week’s lesson expands this knowledge to include all rational numbers. This lesson is based on the work done in 6th grade with addition/subtraction of positive fractions in conjunction to the work done with addition/subtraction of integers.
Continue working with students on Mathematical Practice #7, looking for and making use of structure. The success of this lesson depends on the students’ ability to connect the structure that helped them develop their strategies/algorithms in week 1 and their prior know of fractional addition/subtractions. It is an opportunity time to introduce Mathematical Practice #2, reason abstractly and quantitatively. Both reference books, Oncore Mathematics and Mastering the Common core, will provide real world problems in order to support the deep and application of addition/subtraction of rational numbers.
Background Information
Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials at http://www.azed.gov/educator-certification/
Assessment:
Product
- This will be an ongoing product that will be developed during each week of the unit. Continue foldables this week with long division.
FoldableMake a foldable with five divided sections (3 pieces of paper needed). Students will create a section for each of the following:
Key Questions
Observable Student Behaviors
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Vocabulary:
Fractions Integers Negative Numbers
Number Line Opposites Positive Numbers
Suggested Activities:
Highly Recommended
Diverse Learners:
Homework:
Terminology for Teachers:
Lesson Plan in Word Format (Click Cancel if asked to Log In)
Resources:
Professional Texts
Literary Texts
- Fractions
- http://sci.tamucc.edu/~eyoung/fractions_literature.html
- Less Than Zero (MathStart 3) Stuart J. Murphy
- Perry the Penguin needs 9 clams to buy an ice scooter -- but he's not very good at saving. As Perry earns, spends, finds, loses, and borrows clams, a simple line graph demonstrates the concept of negative numbers.
- http://www.amazon.com/exec/obidos/tg/detail/-/0060001267/qid=1088704854/sr=1-2/ref=sr_1_2/002-0537282-1976045?v=glance&s=books
Mathematics in Children's Literature:- Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annotated Lists of Children's Literature including the math concepts and grade levels.
- Click on the following link, http://libguides.nl.edu/mathinchildrenslit, then look under Math and Literature Bibliographies.
- Lost in Lexicon: An Adventure in Words and Numbers by __Pendred Noyce__ and Joan Charles (Jul 26, 2011)
- "If this is an adventure, we should just plunge in..."
- When thirteen-year-old cousins Ivan and Daphne go on a treasure hunt in the rain one summer day, they never expect to stumble into a whole new world where words and numbers run wild. After the cousins outwit a plague of punctuation, grateful villagers beg them to find Lexicon's missing children, who have been enticed away by dancing lights in the sky. Trekking between villages in search of clues, the cousins encounter a talking thesaurus, a fog of forgetting, the Mistress of Metaphor, a panel of poets, feuding parts of speech, and the illogical mathematicians of Irrationality. When a careless Mathemystical reflects them across the border into the ominous Land of Night, their peril deepens. Kidnapped, imprisoned, and mesmerized—with time running out—will Ivan and Daphne find a way to solve the mystery of the lights in the sky and restore the lost children of Lexicon to their homes? Lost in Lexicon will whisk children away into an interactive and magical world of learning.
- 101 Things Everyone Should Know About Math by __Marc Zev__, __Kevin Segal__ and Nathan Levy (Mar 16, 2010) (real world)
- Math is a critical part of our everyday lives; we use it dozens of times daily and wish we understood it better. The second title in the 101 Things Everyone Should Know series, this book makes understanding math easy and fun! Using an appealing question and answer format, this book is perfect for kids, grown-ups and anyone interested in the difference between an Olympic event score of 9.0 and Richter scale score of 9.0.
Middle & High School: Literature in MathematicsMany books include websites with lesson ideas. http://sci.tamucc.edu/~eyoung/middle_school_literature.html
Lesson Plans for Using Literature in Middle and High School Mathematics (developed by Leonor and edited by Elaine)
- http://sci.tamucc.edu/~eyoung/Literature%20webpages/Leonor/index.html
Miscellaneous Math and Children's LiteratureInformational Texts
Art, Music, and Media
Manipulatives
Games
Videos
Discovery Learning
- http://www.discoveryeducation.com/
The teaching Channel currently offers videos of K-12 mathematics teaching aligned with the Common Core Sate Standards, which would be perfect for professional development with teacher teams.SMART Board, Promethean Lessons
- Smart Board rational number lessons
http://exchange.smarttech.com/details.html?id=1764f052-3804-448f-9f12-95bc5646a2eaRational numbers Smart Board lessons
Other Activities, etc.
Interactivate is a set of free, online courseware for exploration in science and mathematics. It is comprised of activities, lessons, and discussions. The site is structured around collections of activities, lessons, and discussions.
http://www.shodor.org/interactivate/guide/
Activities and tools:
http://www.shodor.org/interactivate/activities/
Utah Education Network
http://www.uen.org/Lessonplan/preview.cgi?LPid=19833
- Commutative Rectangle
http://illuminations.nctm.org/LessonDetail.aspx?ID=L566Students typically learn about the concepts of identity, inverse, commutativity, and associativity by exploring the four basic operations (+, –, ×, and ÷) with integers. In this lesson, students investigate these concepts using a geometric model. Moves are performed with a rectangle, and the results of an operation that combines two moves are analyzed. Students determine if the operation is commutative or associative; if an identity element exists; or if there are inverses for any of the moves.
- Elevator Arithmetic
http://illuminations.nctm.org/LessonDetail.aspx?ID=L733Students will use vertical movement of an elevator to evaluate signed number expressions.
- Flipping for Integers
http://illuminations.nctm.org/LessonDetail.aspx?ID=L734In this lesson, students will adapt expressions that add or subtract two signed integers. This lesson builds on the previous lesson in the unit, where students add/subtract just a positive integer from a signed integer.
- Fun with Baseball Stats
http://illuminations.nctm.org/LessonDetail.aspx?ID=L257The following grades 6-8 activities allow students to explore statistics surrounding baseball. They are exposed to connections between various mathematical concepts and see where this mathematics is used in areas with which they are familiar. This lesson plan is adapted from the May 1996 edition of Mathematics Teaching in the Middle School.
- Power Up
http://illuminations.nctm.org/LessonDetail.aspx?ID=L699Using old batteries and a voltage sensor, students get a real feel of the meaning of negative and positive numbers. Students explore addition of signed numbers by placing batteries end to end (in the same direction or opposite directions) and observe the sum of the batteries’ voltages.
- Battery Lab
http://illuminations.nctm.org/Lessons/PowerUp/PowerUp-AS-Voltmeter.pdfThis reproducible activity, from an Illuminations lesson, features directions and questions that guide students to place batteries end to end and calculate the sum of the batteries' voltages.
- Magic Squares
http://illuminations.nctm.org/LessonDetail.aspx?ID=L263This lesson explores magic squares from both a historical and mathematical perspective. The mathematical analysis leads into symbolic algebraic representation of the patterns. This lesson is based upon an article from the April 2001 edition of Mathematics Teaching in the Middle School.
- Too Big or Too Small?
http://illuminations.nctm.org/LessonDetail.aspx?ID=L252In this lesson, students develop number sense through a series of three hands-on activities. Students explore the following concepts: the magnitude of a million, fractions between 0 and 1, and the effect of decimal operations.
- Volt Meter
http://illuminations.nctm.org/ActivityDetail.aspx?ID=152This student interactive, from an Illuminations lesson, allows students to learn about positive and negative numbers by exploring the voltage of batteries.
Language
Arts
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
7 Matrix
Accelerated 7
Matrix
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Home K-2
Home 3-6
Home 6-8
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6